This invention relates to a transmission device between a primary drive shaft and an output shaft, such as a wheel drive shaft, of an automotive machine, such as a lawnmower, of the type comprising a housing inside of which is housed at least partially a reduction gear mechanism that consists of an engine-driving element, such as an endless screw, meshed with a driven element, such as a gearwheel, whereby the driven element is likely to be coupled to or uncoupled from said output shaft by means of a clutch mechanism that is activated/deactivated by axial movement of the gearwheel on the shaft, this movement being controlled by an actuating element that can be moved angularly, such as a fork, as well as a vehicle that is equipped with such a transmission device.